Narrow-Band Frequency Filters and Splitters, Photonic Sensors, and Cavities Having Pre-Selected Cavity Modes

ABSTRACT

Waveguides and electromagnetic cavities fabricated in hyperuniform disordered materials with complete photonic bandgaps are provided. Devices comprising electromagnetic cavities fabricated in hyperuniform disordered materials with complete photonic bandgaps are provided. Devices comprising waveguides fabricated in hyperuniform disordered materials with complete photonic bandgaps are provided. The devices include electromagnetic splitters, filters, and sensors.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationNo. 61/547,480 filed on 14 Oct. 2011 and entitled “Cavity and WaveguideArchitectures in Hyperuniform Disordered Materials with CompletePhotonic Bandgaps, and to U.S. patent application Ser. No. 13/379,740filed on 21 Dec. 2011 and entitled “Non-Crystalline Materials HavingComplete Photonic, Electronic or Photonic Bandgaps,” which is anationalization of international patent application numberPCT/US10/39516 filed on 22 Jun. 2010 of same title, which claimspriority to U.S. Provisional Patent Application No. 61/269,268 filed on22 Jun. 2009 of same title.

FIELD OF INVENTION

The disclosure relates to hyperuniform disordered materials withcomplete photonic band gaps adapted to support elements of integratedelectromagnetic circuits including, without limitation, electromagneticcavities and waveguides having novel architectures.

BACKGROUND

Familiar elements of photonic and phononic systems such as waveguides,splitters, resonant cavities, and frequency filters are realized inmaterials in which photonic or phononic bandgaps exist or can befabricated. Waveguides in photonic crystalline arrays (photoniccrystals) have been proposed for many photonic applications, butphotonic crystals have the disadvantage that they are highlyanisotropic, placing tight constraints on the bending angles forwaveguides and prohibiting any waveguide sections that do not align withthe high symmetry directions in the crystal. Cavities in photoniccrystals have also been proposed and fabricated for use in many photonicapplications but, again, confinement of the radiation is anisotropic,making the properties of the cavities more difficult to control andintroducing losses (leakage of the radiation). The photonic environmentoffered by crystalline material provides the strongest confinement alongthe high-symmetry directions of the crystal (along which are placedscattering centers), but is less effective along the other directions.

Phononic crystals are analogous to photonic crystals in that they arefashioned from inhomogeneous materials characterized by periodicvariations in their mechanical properties (Sigalas, M., and Economou, E.J. Sound Vib. 158: 377-382, 1992). The electrical and magnetic wavesthat traverse photonic crystals (except in photonic bandgaps) areanalogous, in some ways (Estrada, H. et al., Phys. Rev. Lett. 102:144301, 2009) to the acoustic and elastic waves that traverse phononicmaterials (except in phononic bandgaps)

SUMMARY

In one embodiment, the invention provides a designed cavity fabricatedin a hyperuniform disordered photonic material having a completephotonic bandgap (i.e., neither electrical or magnetic waves propagate),wherein the cavity confines a photon.

In another embodiment, the invention provides a designed cavityfabricated in a hyperuniform disordered phononic material having acomplete phononic bandgap (i.e., neither acoustic nor elastic wavespropagate), wherein the cavity confines a phonon.

In another embodiment, the invention provides a designed waveguidefabricated in a hyperuniform disordered photonic material having acomplete photonic bandgap, wherein the waveguide confines thepropagation of a photon.

In another embodiment, the invention provides a designed waveguidefabricated in a hyperuniform disordered phononic material having acomplete phononic bandgap, wherein the waveguide confines thepropagation of a phonon.

In other embodiments, the invention provides a device, either photonicor phononic, comprising a cavity (which may be photonic or phononic) anda waveguide (which may be photonic or phononic) fabricated in ahyperuniform disordered material (photonically or phononicallyresponsive, as appropriate) having a complete bandgap.

In some embodiments, the aforementioned device comprises a plurality ofwaveguides disposed at arbitrary angles with respect to one another andin electromagnetic or phononic communication, as appropriate. In oneembodiment, the communication takes place at a junction of thewaveguides. In one embodiment, the junction comprises a cavity(electromagnetic or phononic) that communicates with the waveguides andcan have one or more localized cavity modes with pre-selectablesymmetries. In some embodiments, a spectrum of electromagnetic (oracousto-elastic) waves enters through one arm and is divided at thejunction into different frequency bands, each of which is directed intodifferent arms. In some embodiments, at least a first and a second ofthe aforementioned waveguides comprise line defects that differ from oneanother in a way that causes the first and second waveguides to transmitdifferent frequency ranges.

In some embodiments, the device (or an element within a device) sensesthe presence or amount of a substance, which substance may be spacedapart from the device or associated with the device. The substance isexposed to an electromagnetic radiation such that the exposure induces adetectable mode of radiation in the device, wherein said mode isselected from a cavity mode and a waveguide mode, and wherein said modecorrelates to a presence or amount of said substance in a space. Inother embodiments, the device senses a force applied to a target (whichmay be spaced apart from the device or associated with the device)exposed to an electromagnetic radiation such that said device induces adetectable mode of said radiation in said device, wherein said mode isselected from a cavity mode and a waveguide mode and wherein said modecorrelates to a presence or amount of said force at a specifiedlocation. In another embodiment, the device senses a quantity of heatapplied to a target (which may be spaced apart from the device orassociated with the device) exposed to an electromagnetic radiation suchthat said device induces a detectable mode of said radiation in saiddevice, wherein said mode is selected from a cavity mode and a waveguidemode and wherein said mode correlates to a presence or amount of saidheat at a specified location or in a specified space.

In one embodiment, the invention provides a method of detecting apresence or an amount of a substance in a specified location or space byexposing said substance to an electromagnetic radiation to induce adetectable mode of radiation in a device according to other embodimentsof the invention, and correlating said induced mode to said presence oramount.

In one embodiment, the invention provides a method of detecting apresence or an amount of a force applied to a target in a specifiedlocation by exposing said target to an electromagnetic radiation toinduce a detectable mode of radiation in a device according to otherembodiments of the invention, and correlating said induced mode to saidpresence or amount of force applied.

In one embodiment, the invention provides a method of detecting apresence or an amount of a quantity of heat applied to a target in aspecified location or space by exposing said target to anelectromagnetic radiation to induce a detectable mode of radiation in adevice according to other embodiments of the invention, and correlatingsaid induced mode to said presence or amount of said heat.

In the aforementioned methods, the detected mode is detected as a changeselected from the group consisting of phase, frequency, polarization,intensity and dielectric susceptibility, wherein said change isdetermined qualitatively or quantitatively.

A target may “associate” with a material, which may be a photonic orphononic material or otherwise, by binding to the material (e.g.,electrostatically, by means of Van der Waal's forces, etc.), by beingsuspended or dispersed in the material, by covalently combining with thematerial, etc. “Association” herein requires only that the material, byassociating with the target, undergoes a change in one or more of itsproperties, which change is detectable with an electromagnetic oracousto-elastic sensor and is relatable to the presence or amount of thetarget.

GENERAL DESCRIPTION

Photonic band gap (PBG) materials are a class of artificially createddielectric materials that carry the concept of manipulating andcontrolling the flow of light as well as other electromagneticfrequencies. PBG materials typically consist of a dielectricmicrostructure with two interpenetrating dielectric components, in whichthe index of refraction varies on a length scale associated with thewavelength of the radiation to be controlled. Under the rightconditions, these dielectric microstructures allow the formation of aphotonic band gap, a range of frequencies for which electromagnetic wavepropagation is prohibited for all directions and polarizations. Then, byreducing or enhancing the effective dielectric at a certain point, it ispossible to create a localized state of the electromagnetic field. Thiscan be realized, for instance, in a two-dimensional photonic crystalconsisting of dielectric cylinders in air, by removing one of thecylinders or enlarging it or changing its dielectric constant. Due tothe presence of the point-like defect, a localized cavity mode iscreated within the photonic band gap at a certain frequency. For thecavity mode, light and electromagnetic waves in general cannot propagateanywhere outside the cavity since the trapped frequencies are in theband gap of the exterior material. Therefore, by creating the pointdefect, light (or any other electromagnetic wave) is localized on thelength scale of the cavity, approximately the wavelength of the light orother electromagnetic wave. Such cavities have low mode volumes and assuch exhibit very high quality factors (a measure of the confinement ofthe radiation).

Generally, photonic band gaps and the associated cavity localization andwaveguide mechanisms are thought to be an exclusive property of periodicsystems, namely photonic crystals. In this work, we show, in embodimentsof the invention, that there exists a far wider class of cavityarchitectures that are built around hyperuniform disordered pointpatterns. Hyperuniform point patterns include periodic, quasiperiodicand certain disordered systems and are characterized by randomfluctuations in the distribution of components that grow in variance notas surface area but more slowly than the surface area of the domainconsidered in 2d and more slowly than the volume of the domainconsidered in 3d. The cavities and waveguides in hyperuniform photonicstructures can be computer-designed and manufactured using standardfabrication techniques used for photonic crystals and have the abilityof confining and guiding both TM and TE polarized electromagneticradiation, a property once thought to be unique to periodic structures.

Cavities in hyperuniform disordered heterostructures described hereincan be introduced anywhere within the structure and with any isotropicsurrounding material and can allow confinement of the electromagneticradiation in an isotropic way in patterns that can be monopolar,dipolar, quadrupolar or high symmetry within the cavity, as desired,while at the same time the leakage of the localized radiation outsidethe cavity is minimized in all directions.

An embodiment includes a set of devices: new types of waveguidesrealized in hyperuniform disordered materials with complete photonicband gaps.

Waveguide architectures disclosed herein offer advantages over thewidely employed waveguides in photonic crystals for certainapplications, due to their ability to guide the light andelectromagnetic waves of all polarizations through arbitrarily orientedwaveguide pathways (channels) in the material and guide bothpolarizations of the radiation through the same waveguide channel. Thisis because in the case of photonic crystals or quasicrystals, thewaveguiding phenomena strongly depend on the orientation of thewaveguide channels with respect to the high symmetry directions of thecrystal. For hyperuniform disordered structures, there are no suchpreferential directions—all directions are equally preferred—so theconfinement around the bending region is considerably more isotropic.

An embodiment includes use of waveguides realized in hyperuniformdisordered materials with complete photonic bandgaps for photonicapplications where it is important to control the path of a propagatingphoton or electromagnetic wave and to manipulate its energy, momentumand/or polarization (collectively, its “mode”), including optical andother electromagnetic micro-circuits, especially in cases where it isadvantageous to have paths with irregular shapes (not straight). Anembodiment relates to novel types of photon sources that benefit fromthe modification of the photonic density of states due to the presenceof a waveguide, such as single-photon sources.

The photonic environment offered by quasicrystalline heterostructuresare more isotropic, and as such may allow loss-loss bending for widerrange of angles, but they still do not allow lossless bending forarbitrary angles and may be difficult to construct. The waveguides inhyperuniform disordered heterostructures presented here allow low-lossbending for arbitrary angles. In addition, the waveguides are easier toconstruct and manipulate.

The waveguides disclosed herein are realized by modifying the dielectricconstant along arbitrary chosen paths in a hyperuniform disorderedmaterial. The material is a heterostructure consisting of two or morematerials with different dielectric constants. They are examples ofdesigner materials in which the arrangement of the dielectrics iscompletely controlled in the fabrication process. To be hyperuniform,the design is chosen so that the random fluctuations in the distributionof dielectric materials of any type increases as less than the area (in2d) or the circumference times (⅔πr²) (in 3d). Waveguides inhyperuniform disordered arrangements can be incorporated in the computerdesign and then the material can be manufactured using the same standardtechniques used for photonic crystals.

Prototype waveguide channels in hyperuniform disordered materials havebeen fabricated by constructing the proposed architectures consisting ofdielectric cylinders and walls made out of alumina on amillimeter-centimeter scale (Al2O3, with a dielectric constant of 9.61).The experimental measurements of transmission in the microwave regimeare in good agreement with the theoretical predictions.

An embodiment includes use of waveguides realized in hyperuniformdisordered materials with complete photonic bandgaps in most cases wherewaveguides are used with the advantage that they can bend alongarbitrarily oriented pathways. Both TM and TE polarization of light orother electromagnetic waves can be guided along the same waveguidechannel.

Embodiments include a set of devices: new types of photonic cavitiesrealized in hyperuniform disordered materials with complete photonicband gaps. An embodiment includes employing the devices in photonicapplications where it is important to manipulate photons through spatialconfinement and the modification of the photonic density of states dueto the presence of a point-like defect (cavity). Applications mayinclude but are not limited to micro-lasers, devices employing enhancedoptical and other electromagnetic nonlinearities and single-photonsources. An embodiment relates to novel types of light sources thatbenefit from the modification of the photonic density of states due tothe presence of a linear defect (waveguide), such as single-photonsources.

The new cavity architectures herein may offer advantages over the widelyemployed cavities in photonic crystals for certain applications, due totheir ability to confine the light in a statistically isotropic photonicenvironment. Also, unique to these cavities is the simultaneouslocalization of both polarizations of the radiation, TM and TE, in thesame physical structure. In the case of photonic crystals orquasicrystals, the localization phenomena strongly depend on theposition of the cavity within the unit cell: the best confinement isrealized along the high symmetry directions of the crystal, while inother directions the crystal is less effective in confining theradiation. For hyperuniform disordered structures, there are no suchpreferential directions and the confinement is considerably moreisotropic. Calculations demonstrate that by precisely tuning thephysical properties of a cavity in hyperuniform disordered structure, itis possible to accurately control the localized photonic mode patternwithin the cavity and induce a rich variety of spatial symmetries in thespatial distribution of the electromagnetic mode.

The cavities can be realized by modifying the dielectric constant aroundan arbitrary point in a hyperuniform disordered material. The materialis a heterostructure consisting of two or more materials with differentdielectric constants.

They are examples of designer materials in which the arrangement of thedielectrics is completely controlled in the fabrication process. To behyperuniform, the design is chosen so that the random fluctuations inthe distribution of dielectric materials of any type increases as lessthan the area (in 2d) or the circumference times (⅔πr²) (in 3d). Thedielectric materials act as scattering centers for electromagneticradiation. The cavity can be implemented by including in the design thereduction in the size or complete elimination of the scattering centerat that center of the cavity, or by gradually filling one of thescattering cells of the heterostructure with a high-index of refractionmaterial. Due to the presence of this intentional defect, a localizedmode is created within the band gap of the photonic heterostructure andthe electromagnetic radiation can be spatially localized by excitingthis defect mode. The underlying hyperuniform disordered heterostructurein which the defect is introduced must be constructed in a manner thatis hyperuniform; that is, the random fluctuations in the distribution ofcomponents must grow as less than the area (in 2d) or the circumferencetimes ⅔πr² (in 3d).

Full computer simulations of cavities in two-dimensional structures andthree-dimensional structures with axial symmetry have demonstrated theirability to localize the electromagnetic radiation using the samecomputer algorithms that accurately predict the photonic cavityproperties for photonic crystals and quasicrystals. Prototypes for thehyperuniform disordered materials without defects and with waveguidedefects have been constructed and experimental results with the sameagree with the computer simulations. Since simulations and experimentsagree well in these two cases, and there is no new physics involved withthe cavities, simulations and experiments should work well with cavitiesas well.

An embodiment includes use of cavities realized in hyperuniformdisordered materials with complete photonic bandgaps in most cases wherecavities are used, with the advantage that they can confine theradiation in a more isotropic way and can realize confined modesexhibiting a variety of symmetries. Both TM (transversal magnetic) andTE (transversal electric) polarization of light can be confinedisotropically in the same physical structure.

Hyperuniform disordered solids herein may have an advantage in that theyare less sensitive to fabrication defects since they are disordered tobegin with. This advantage may mean that fabricating waveguides andcavities as described herein is easier.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawings will be provided by the Office upon request and paymentof the necessary fee.

The following detailed description of the preferred embodiments of thepresent invention will be better understood when read in conjunctionwith the appended drawings. For the purpose of illustrating theinvention, there are shown in the drawings embodiments which arepresently preferred. It is understood, however, that the invention isnot limited to the precise arrangements and instrumentalities shown. Inthe drawings: The drawings filed herewith include illustrations ofphotonic cavities and waveguides and are incorporated herein as if fullyset forth.

FIG. 1 shows the design of a hyperuniform disordered structure andphotographs in side view and top view.

FIG. 2 shows the measured transmission spectrum and calculatedtransmission and density of state (DOS) for the hyperuniform sample.

FIG. 3 shows photographs of wave-guiding channels and plots ofTM-polarized transmission therethrough.

FIG. 4 shows the Finite Difference Time Domain (FDTD) simulations of(left) TM and (right) TE band structures (blue and red curves) andDensity of States (DOS) (green curve) for the structure shown in FIG. 1.

FIG. 5 shows the measured transmission as a function of frequencies(f=r) and incident angles (θ=θ) for square lattice of (r=2.5 mm, t=0.38mm, a=13.3 mm).

FIG. 6 shows electric field distributions in point defects that form asinusoidal waveguide in a hyperuniform disordered structure.

FIG. 7 shows a photograph of a “Y” junction for frequency splitting andplots of transmission vs. frequency for each branch.

FIG. 8 shows 2-step and 3-way frequency splitters and plots oftransmission vs. frequency for each guide path.

FIG. 9 shows electric field distributions for cavity modes of differentsymmetries obtained by changing the size of the defect.

FIG. 10 is a photograph of a hyperuniform disordered structure showingthe experimental setup for interrogating a slice of the structure.

FIG. 11 is a plot of TM polarization transmission through slices ofvarying thickness.

FIG. 12 is a plot of TM polarization transmission for various rodconfigurations.

FIG. 13 is a photograph of a filtering waveguide showing particularcavity mode modifications and a plot of TM polarization transmissionsfor each modification.

FIG. 14 shows higher order modes in the waveguide channel of FIG. 6.

FIG. 15 shows a photo of and transmission profiles through a 50° bend inan experimental waveguide.

FIG. 16 A-B shows a simulated cavity mode obtained by removing one ofthe dielectric cylinders (FIG. 16a ) contrasted to an unperturbedhyperuniform disordered structure (FIG. 16b ).

FIG. 17 shows the electric field mode distribution as calculated for afew selected localized modes.

FIG. 18 shows the evolution of the localized modes associated with adefect cylinder as a function of the dimensionless defect radius.

DEFINITIONS

To facilitate an understanding of the various embodiments of thisinvention, a number of terms (which may be set off in quotation marks inthis Definitions section) are defined below. Terms used herein (unlessotherwise specified) have meanings as commonly understood by a person ofordinary skill in the areas relevant to the present invention. As usedin this specification and its appended claims, terms such as “a”, “an”and “the” are not intended to refer to only a singular entity, butinclude the general class of which a specific example may be used forillustration, unless the context dictates otherwise. For example, thephrase “chosen from A. B, and C” and the like, as used herein, meansselecting one or more of A, B, C. The phrase “at least one” followed bya list of two or more items, such as “A, B, or C,” means any individualone of A, B or C as well as any combination thereof. Certain terminologyis used in the following description for convenience only and is notlimiting.

As used herein, absent an express indication to the contrary, the term“or” when used in the expression “A or B,” where A and B refer to acomposition, product, etc., means one or the other, or both. As usedherein, the term “comprising” when placed before the recitation of stepsin a method means that the method encompasses one or more steps that areadditional to those expressly recited, and that the additional one ormore steps may be performed before, between, and/or after the recitedsteps. For example, a method comprising steps a, b, and c encompasses amethod of steps a, b, x, and c, a method of steps a, b, c, and x, aswell as a method of steps x, a, b, and c. Furthermore, the term“comprising” when placed before the recitation of steps in a method doesnot (although it may) require sequential performance of the listedsteps, unless the context clearly dictates otherwise. For example, amethod comprising steps a, b, and c encompasses, for example, a methodof performing steps in the order of a, c, and b; c, b, and a, and c, a,and b, etc.

Unless otherwise indicated, all numbers expressing quantities ofingredients, properties such as molecular weights, reaction conditions,etc., as used in the specification and claims, are to be understood asbeing modified in all instances by the term “about.” Accordingly, unlessindicated to the contrary, the numerical parameters in the specificationand claims are approximations that may vary depending upon the desiredproperties sought to be obtained by the present invention. At the veryleast, and without limiting the application of the doctrine ofequivalents to the scope of the claims, each numerical parameter shouldbe construed in light of the number of reported significant digits andby applying ordinary rounding techniques. Notwithstanding that thenumerical ranges and parameters describing the broad scope of theinvention are approximations, the numerical values in the specificexamples are reported as precisely as possible. Any numerical value,however, inherently contains standard deviations that necessarily resultfrom the errors found in the numerical value's testing measurements.

The term “not,” when preceding and made in reference to any particularnamed composition or phenomenon, means that only the particularly namedcomposition or phenomenon is excluded.

The term “altering” and grammatical equivalents as used herein inreference to the level of any substance and/or phenomenon refers to anincrease and/or decrease in the quantity of the substance and/orphenomenon, regardless of whether the quantity is determinedobjectively, and/or subjectively.

The terms “increase,” “elevate,” “raise,” and grammatical equivalentswhen used in reference to the level of a substance and/or phenomenon ina first instance relative to a second instance, mean that the quantityof the substance and/or phenomenon in the first instance is higher thanin the second instance by any amount that is statistically significantusing any art-accepted statistical method of analysis. Correspondingly,the terms “reduce,” “inhibit,” “diminish,” “suppress,” “decrease,” andgrammatical equivalents when used in reference to the level of asubstance and/or phenomenon in a first instance relative to a secondinstance, mean that the quantity of substance and/or phenomenon in thefirst instance is lower than in the second instance by any amount thatis statistically significant using any art-accepted statistical methodof analysis.

The terms “photon” and “phonon,” strictly speaking, are terms of art inquantum mechanics. Herein, however, since all embodiments of theinvention are based on classical mechanical principles, the terms areused interchangeably with their counterparts in classical mechanics,viz., “electromagnetic wave” (“light” if the wave is in the visiblespectrum) and “acousto-elastic wave” (“sound” if the wave is in therange of human audition), respectively.

The term “photonic material” relates to a substantially transparentmaterial characterized by having local dielectric contrasts distributedwithin the material, which contrasts cause electromagnetic waves/photonsentering the material to be reflected, refracted, absorbed, dispersed orotherwise affected, with the result that certain frequencies of theimpinging waves/photons may not exit the material but may be retained aswaves/photons within the material. It will be understood that theelectromagnetic waves/photons discussed herein may be referred to as“light” or “light waves” whether or not the frequencies of theparticular waves/photons being referred to are in the visible part ofthe spectrum.

The term “band” refers to a finite range of electromagnetic waves oracousto-elastic waves of different frequencies within theelectromagnetic or acousto-elastic spectrum. When a subset thereof isabsent from the band, a “band gap” (band-gap, bandgap) exists. Sincephotonic and phononic materials create such gaps by prohibiting passageof a range of frequencies within the band (a “sub-band”), the term“bandgap” often is used in reference to the material, not to the absentwave energy. Herein, the term may refer to either one, as the context soadmits.

The term “complete bandgap” (or “absolute bandgap”) in the context ofelectromagnetic radiation (which comprises electrical and magnetic wavesin a mix of polarizations) means a band from which both types of waveare absent. In the context of acousto-elastic waves in solids, the termmeans a band from which acousto-elastic waves oscillating in thedirection of propagation and acousto-elastic waves oscillatingtransverse to the direction of propagation are both absent.Equivalently, the term refers to a photonic element in a photonicmaterial within which neither an electrical or a magnetic wave (having aparticular frequency and direction) is allowed passage, or to a phononicelement in a phononic material within which neither a longitudinal nor atransverse wave is allowed passage. It is understood that the bulkmaterial outside the photonic or phononic element forbids passage ofwaves (at least within a band).

The term “photonic element” refers to one or more of the localdielectric contrasts in a photonic material or to a region(s) in thematerial from which dielectric contrast has been removed orquantitatively altered. Manipulation of photonic elements leads toconfigurations that variously confine (“trap” or “guide”) waves/photonswithin the material, sometimes to practical effect. Therefore, the term“photonic element” may refer generically to such configurations. Thus,“waveguides,” “resonant cavities,” “photonic filters,” and “photonicsplitters” are photonic elements.

The term “phononic element” refers to one or more of the local contrastsin a mechanical property of a phononic material or to a region(s) in thematerial from which the mechanical contrast has been removed orquantitatively altered. Manipulation of phononic elements leads toconfigurations that variously confine (“trap” or “guide”)acousto-elastic waves within the material, sometimes to practicaleffect. Therefore, the term “phononic element” may refer generically tosuch configurations. Thus, “waveguides,” “resonant cavities,” “phononicfilters,” and “phononic splitters” are phononic elements.

The term “in photonic communication” refers to a condition wherein afirst photonic element can receive from or transmit to a second photonicelement a photon/electromagnetic wave. Similarly, “in phononiccommunication” refers to a condition wherein a first phononic elementcan receive from or transmit to a second phononic element anacousto-elastic wave.

The term “photonic cavity” as used herein relates to a device (or anelement within a device) realized in a material that prohibitspropagation in at least one direction of either the electrical or themagnetic component, or both, of electromagnetic radiation (energeticparticles or waves that are capable of self-propagating in a vacuum atone or more frequencies, the cavity characterized in that it can containor “trap” within it at least one state or mode of that electromagneticradiation. That is, the radiation can enter the cavity (and sometimesresonate therein) but cannot propagate out of the cavity. When aheterostructure assembled from two types of “building blocks,” each typecontrasting in refractive index, is perturbed by removing or adding asingle block, a “point defect” is created. If that defect is locatedwithin a band-gap region of the assembly, it can create a cavity inwhich the photonic wave/particle remains confined, theoreticallyforever. The term “phononic cavity” is intended to convey the sameconcept, except that the trapped mode comprises an acousto-elastic wave.

The term “mode” relates to a state or configuration of electromagneticor acousto-elastic waves, the state characterized by an energy, amomentum and a polarization.

Localized modes, wherein propagation is not allowed, may exhibit various“mode symmetries” (e.g., monopole, dipole, quadrupole, etc.) dependingupon the number and shape of the fields generated by the “back andforth” travel from one edge of a cavity to another of the trappedwave(s).

The term “electromagnetic waveguide” as used herein relates to a device(or an element within a device) realized as a channel in a material thatprohibits propagation of one or more polarizations (electromagneticradiation comprises an integrated electrical and a magnetic componentseparated as polar opposites) at one or more frequencies, the waveguidecharacterized in that it can contain and allow the propagation thereinof at least one state or mode of that electromagnetic radiation(otherwise prohibited in the material), not unlike an electromagneticcavity. Waveguides, however, allow certain modes to travel through andout of the guide path. Waveguides are created by designing and arranginga “line” of point defects in a bandgap region of a heterostructure.Similarly, phononic waveguides contain and allow the propagation thereinof at least one state or mode of acousto-elastic radiation.

The term “electromagnetic polarization” relates to the fact thatelectromagnetic radiation is a combination of a time-varying electricaland magnetic impulse, each oscillating in a plane of its own. The planesare disposed orthogonally to each other, which means that the electricalwave is maximally separated from the magnetic wave, i.e., the waves are“polarized.” The intersection of the planes describes the direction ofthe radiation. The planes are oriented transverse to the direction ofradiation. Thus, the radiation is polarized into a “transverseelectrical” mode and a “transverse magnetic” mode. In a waveguide, onlyoscillations that “fit” within the boundaries of the channel can exist.Guided radiation, therefore, will not pass through the channel at anyfrequency that is disallowed because its transverse electrical wavedoesn't fit or because its transverse magnetic wave doesn't fit. In thecontext of acousto-elastic waves in solids, polarization refers to thefact that the waves can oscillate in the direction of wave propagationor transverse to the direction of propagation.

The term “splitter” as used herein relates to a plurality of waveguidesconfigured to meet at a junction, optionally with an associated cavity,in a bulk material that prohibits the propagation of radiation for afinite range of frequencies. The waveguides are in electromagnetic (oracousto-elastic) communication. In preferred embodiments, the junctionis designed such that a mixture of waves, prohibited in the bulkmaterial, can enter one arm and then be divided by frequency as thedesigner so determines. Also as the designer so determines, the dividedwaves can be directed into the other arms. An arbitrary number ofbranches is contemplated and a branch angle may approach 0° at oneextreme and 180° at the other.

The energy, momentum and/or polarization state of the radiation, may bedetected as a change in phase, frequency, or intensity.

The states or modes of radiation that are allowed to pass into the otherarms may be determined by the energy, momentum and polarization of theradiation to affect its phase, frequency and intensity.

The term “filter” relates to a device (or an element within a device)that selects a spectrally narrow range of frequencies out of a broadincoming range of frequencies to create a first, narrow band and asecond band, different from the broad incoming band because of theextraction, by splitting, of the first band. Depending upon theapplication, the narrow-band may be selected for further use and therest of the incoming frequencies reflected or absorbed (a “band-pass”filter). In a “stop-band filter” one or more narrow bands arereflected/absorbed and the rest of the incoming frequencies aretransmitted for further use.

The term “electromagnetic sensor” relates, in one aspect, to a device(or an element within a device) for sensing the presence or amount of aparticular target substance in a specified location or space or time. Inanother aspect, the term relates to a device (or an element within adevice) for sensing the presence or amount of a force applied to atarget. In another aspect, the term relates to a device (or an elementwithin a device) for sensing the presence or amount of heat in aspecified location or space. In some embodiments, the target substanceor the applied force or heat induces (or quenches) a detectable cavitymode in the electromagnetic radiation. In some embodiments, the targetinduces (or quenches) in the device a detectable waveguide mode in anelectromagnetic radiation. In general, the target or the applied forceor the heat induces a change in the energy, momentum and/or polarizationstate of the radiation, which may be detected as a change in phase,frequency, or intensity of the radiation in the device. A “phononicsensor” operates similarly, except that acousto-elastic radiation isemployed instead of electromagnetic radiation.

A target may “associate” with a photonic or phononic material by bindingto the material (e.g., electrostatically, by means of Van der Waal'sforces, etc.), by being suspended or dispersed in the material, bycovalently combining with the material, etc. “Association” hereinrequires only that the material, by associating with the target,undergoes a change in one or more of its electromagnetic properties,which change is detectable with an electromagnetic sensor and isrelatable to the presence or amount of the target.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Until recently, photonic band gaps and the photon-confining cavities andwaveguides that can be created within them were thought to requirematerials (photonic crystals and certain quasicrystals in particular)characterized by a periodically repeating internal structure. Band gapsoccur in crystals only in severely proscribed orientations.Quasicrystals can relax this constraint of anisotropy that limits theversatility of crystals for use in photonic systems, without at the sametime foreclosing on the possibility of constructing complete (i.e.,“absolute”) band-gaps therein. Because the photonic environment offeredby quasicrystalline heterostructures is more isotropic than that ofcrystals, a photonic confinement cavity in a quasicrystal can trap waveenergies entering the cavity from a wider variety of angles thancorresponding cavities in crystals can. Similarly, waveguides inquasicrystals may be “bent” over a larger selection of bend angles thanwaveguides in crystals, and still transmit losslessly or with low loss.Quasicrystals do not allow lossless bending for arbitrary angles,however, even if scattering elements with very high refractive index areselected for the construction of the quasicrystal. Quasicrystals havebeen designed by placing light-scattering centers at points distributedquasiperiodically in two dimensions (U.S. Pat. No. 8,243,362) and inthree-dimensions (U.S. Pat. No. 8,064,127). U.S. Pat. Nos. 8,243,362 and8,064,127 are incorporated herein by reference for all purposes as iffully set forth herein.

More recently, materials that have their light-scattering centersdistributed in a somewhat disordered manner in a pattern that deviatesfrom both the periodic and the quasiperiodic have been designed (WO2011/005530, incorporated herein by reference for all purposes as iffully set forth herein). Such materials further relax the anisotropyconstraint (essentially to zero under certain specified conditions)without denying the designer the opportunity to construct complete bandgaps therein. The arrangement of scattering centers in periodic andquasiperiodic systems referred to in U.S. Pat. Nos. 8,064,127, 8,243,362and in the disordered systems disclosed in WO 2011/005530 share thestatistical property of hyperuniformity (defined infra).

Non-hyperuniform disordered three-dimensional (“3D”) photonic solidshave been discussed (Edagawa, K. et al., Phys. Rev. Lett 100: 013901,2008; Imagawa, S., et al., Phys. Rev. Lett 82: 115116-1, 2010), butsystematic convergence tests using samples of increasing size would needto be performed to determine whether or not bandgaps can actuallypersist in that type of disordered environment and whether or not any ofthem (if any exist) could be complete, that is, capable of prohibitingthe transmission of both the magnetic wave that oscillates in a firstplane transverse to the direction of propagation (TM) and the electricalwave that oscillates in a second plane also transverse to the directionof propagation but disposed orthogonally to the first plane (TE).

Knowledge that one can create materials that are disordered butnevertheless exhibit complete bandgaps does not carry with it anysubstantive assurance that functional electromagnetic devices can befabricated in disordered materials, hyperuniform or otherwise. Given thereflection, back-scatter, leakage and other quality factor problems thatsuch disorder would suggest to persons skilled in the art, effectivewaveguides, microcavities, filters, resonators, lasers, switches,modulators, etc. of any kind might seem beyond reach, not to mentionwaveguides that bend or join at arbitrary angles, or resonant cavitieswith selectable cavity mode symmetries. Discouraging to the notion thatwaveguides or cavities—particularly ones this versatile—could befabricated in the face of such disorder are at least the followingfacts: Disorder in periodic systems “shrinks” bandgaps (Ryu, H. et al.,Phys. Rev. B 59: 5463, 1999) and can close them entirely (Meisels, R. etal. 1. Optics A: Pure and Applied Optics 9: S396, 2007). Also, it iswell documented that disorder has a deleterious effect on waveguiding(Hughes, S. et al. Phys. Rev. Lett. 94: 033903, 2005) and on the qualityfactor of confinement cavities (Gerace, D. and Andreani, L., Photon.Nanostruct. Fundam. Appl. 3: 120, 2005).

Applicants have experimentally demonstrated an isotropic completephotonic bandgap in a 2D disordered hyperuniform dielectric material(dielectric contrast of 8.76) that has no long-range translational orderand shows no Bragg scattering. Surprisingly, given the foregoing,Applicants have shown that the artisan can, in fact, exploit the bandgapcapabilities and the isotropy of the material to create novel functionalwaveguides of arbitrary shape, as well as cavities with selectablecavity modes in an environment of constrained disorder. Further, thefreeform waveguides can channel photons robustly in arbitrary directionswith facile control of transmission bandwidth and sharp filtering.Finally, the waveguides can be decorated to produce sharp resonantstructures. Accordingly, embodiments comprising such elements, includingnew devices and uses thereof, are described and claimed herein.

Hyperuniform disorder. The concept of hyperuniformity was firstintroduced as an order metric for ranking point patterns according totheir local density fluctuations at large length scales (Torquato, S.and Stillinger, F., Phys. Rev. E 68: 04113, 2003). A point pattern inreal space is hyperuniform if the number variance a(R)² within aspherical sampling window of radius R (in d dimensions), grows moreslowly than the window volume for large R, i.e., more slowly than R^(d).In the context of the disordered networks of dielectric cylinders andwalls that comprise embodiments of the invention, examples of whichembodiments are the experimental samples investigated herein, eachcylinder is connected to three neighbors (trivalency) and thehyperuniformity condition is generated by placing the axial centers ofthe cylinders or rods on a point pattern in which the number variance ofpoints in a “window” of radius R, where σ(R)={N_(R) ²}−{N_(R)}², isproportional to R. Crystalline and quasicrystalline point patternstrivially satisfy this property but, as noted supra, it is also possibleto have isotropic, disordered hyperuniform point patterns. In Fourierspace, hyperuniformity means the structure factor S(k) (a determinant ofthe extent to which a dielectric structure scatters light) approacheszero as |k|→0. k is the momentum of the wave. The hyperuniform patternsthat are relevant here are restricted to the subclass in which randomfluctuations of the pattern in the domain under consideration cause thenumber variance to grow like the window surface area for large R, e.g.,a²(R)=ΛR in two-dimensions, or a²(R)=ΛR² in three dimensions, up tosmall oscillations (Torquato, S. and Stillinger, F., Phys. Rev. E 68:04113, 2003; Zachary, C. and Torquato, J., J. Stat. Mech.: Theory Exp.P12015, 2009). The photonic design pattern of hyperuniform disorderedmaterials (such as the samples investigated herein) has uniform nearestneighbor connectivity, hyperuniform long-range density fluctuationssimilar to crystals and, at the same time, random positional order. Thecombination results in a circularly symmetric diffuse structure factorS(k) similar to a glass, but with the property that S(k) approaches zeroas |k|→0.

By further constraining the disorder, one can produce hyperuniform“stealthy” point patterns for which the structure factor S(k) isisotropic and precisely equal to zero for a finite range of wavenumbers0≤k≤k_(C) for some positive critical wavevector, k_(C). Embodiments ofthe invention are not limited by any theory as to how the embodimentswork, but it is believed that, combined with the condition that thestructure be derived from a point pattern, increasing k_(C) results in anarrowing of the distribution of nearest-neighbor distances. The neteffect is to increase the bandgap so that one obtains the largest bandgaps for a given dielectric constant (Florescu et al., PNAS 106: 20658,2009). Point patterns that conform to any chosen statistical parametercan be computer-designed by methods well-known to persons skilled in theart. Hyperuniform photonic materials may then be constructed bydecorating the point pattern (in this case a hyperuniform stealthypattern) with dielectric materials according to the protocol describedin Florescu, M. et al., PNAS 106: 20658, 2009 and outlined in WO2011/005530. Manufacturing techniques to perform the “decoration” stepsare well-known in the art. The hyperuniform disordered photonicmaterials display an unusual combination of physical characteristicsthat can be exploited in various embodiments of the invention describedand claimed herein. These include statistical isotropy, multiplescattering resulting in localized states, and large, robust, completebandgaps.

A wide variety of “decoration” materials are suitable. Materials will beselected by persons of skill in the art to meet fabrication constraintsfor the wavelength regime of interest and to comport with the nature ofthe energy (vibrational, electronic, photonic) whose transmission is tobe controlled. Photonic crystals (periodic) having structural elementsas small as the nanometer range have been fabricated (e.g., U.S. PatentAppl. No. 2008/0232755, incorporated herein by reference for allpurposes as if fully set forth). Photonic devices that embody aspects ofthe invention preferably comprise materials of relatively highdielectric constant, but hyperuniform disordered structures tend to beless demanding in this respect than quasicrystals.

Samples for investigative use herein were fabricated with commerciallypurchased Al₂O₃ cylinders and walls cut to designed heights and widths.The dimensions of the cylinders and walls and their spacings are notcritical in any absolute sense. The values can be re-scaled together tofix the frequency range of the photonic band-gap that is optimal for agiven embodiment and in part on the preferred dimensions of the devicein which the bandgap is being deployed. The hyperuniform point patternson which the samples were built were generated by the collectivecoordinate method set forth in Torquato, S. and Stillinger, F., Phys.Rev. E 68: 04113, 2003 with stealthy order parameter χ=0.5. A typicalPBG size for structures with χ=0.5 is Δω/ωC=37%, where ωC is the centralfrequency of the gap. For simplicity, PBGs for transverse magnetic (TM)polarized radiation were considered in the illustrative embodimentsexemplified herein. The same analysis for transverse electric (TE)polarized radiation is well within the capability of the skilledartisan.

Data on the first physical realization of a hyperuniform stealthy design(FIG. 1) are presented herein. FIG. 1(a) shows a section of thecylinders and wall network that decorate the 2D hyperuniform disorderedstructure investigated. The area highlighted in the red box is the exactstructure used for the study. FIG. 1(b) and FIG. 1(c) are side view andtop view photographs of the Al₂O₃ cylinders and walls assembled inaccordance with the hyperuniform disordered design. Interactions of thestructure with electromagnetic radiation are given in the Examples,infra. Other physical realizations are readily achieved simply byremoving and replacing cylinders and walls in conformity with theprocedures described herein.

It is to be noted that the use of Al₂O₃ and air is not limiting. Anymaterials that create a dielectric contrast and are otherwise suitablefor fabricating cylinders, sheets, foils, etc. are candidates In air,alumina, silicon, silicon nitride, gallium arsenide, indium phosphide,silica, indium antimonide (for mid infra-red frequencies) and galliumphosphide could apply, among others, including metals (titanium, forexample) embedded in acrylate or similar polymers.

Waveguides, splitters and frequency filters. In contrast to photoniccrystals, where waveguides are limited in their direction and angularityby crystal symmetries (Lin, S-Y et al., Science 282: 274, 1998), theexperimental samples studied herein easily accommodate channels witharbitrary bending angles. It is also easy to decorate their sides,corners and centers with cylinders and walls for tuning and optimizingthe transmission bands. FIG. 3(d) shows a waveguide with a sharp 50°bend made by removing cylinders and walls in a path ˜2a wide. FIG. 3(e)shows the measured transmission. The transmission is comparable to thatin the straight channel with unity transmission despite the sharp bend,and it is adjustable by modifying defects. Even more remarkable is the“S” shaped freeform waveguide shown in FIG. 3(f). As in the otherchannel designs, the transmitting and receiving horns are parallel tothe input and output of the channel and the transmission is of orderunity (FIG. 3(g). Again, transmission bands can be easily improved andflexibly tuned using defect cylinders.

The channels function in a 2D disordered hyperuniform dielectricmaterial with an isotropic complete PBG (all angles angles ofpropagation in the plane and all polarizations). The disordered andhyperuniform material lacks long-range translational order and exhibitsno Bragg scattering, but nevertheless results in isotropic photonicbandgaps. These bandgaps, furthermore, support freeform waveguides thatare impossible to fabricate in photonic crystals. The waveguideembodiments of the invention channel photons robustly in arbitrarydirections with facile control of transmission bandwidth (whichfacilitates filtering), and have the ability to guide both polarizationsof radiation through the same waveguide channel. Moreover, as notedsupra, the waveguides can be decorated to produce sharp resonantstructures. The potential of photonic, phononic and electronic devicesfashioned in hyperuniform disordered structures is thus demonstrated,opening the way for novel application to technologies including but notlimited to displays, lasers (Cao, H. et al., Phys. Rev. Lett. 82: 2278,1999), sensors (Guo, Y. et al., Optics Express 16: 11741, 2008),telecommunication devices (Noda, S. et al., Nature 407: 608, 2000, andoptical micro-circuits (Chutinan, A. et al., Phys. Rev. Lett. 90:123901, 2003).

By way of example but not of limitation, U.S. Pat. No. 6,990,259(incorporated herein by reference for all purposes) describes a photoniccrystal defect cavity biosensor, and its construction and use. Thefindings disclosed herein by Applicants show that defect cavities inhyperuniform disordered materials perform as well or better.Accordingly, defect cavity biosensors constructed as taught in U.S. Pat.No. 6,990,259 but employing hyperuniform disordered materials instead ofperiodic crystalline materials are expected to be used in the same wayto good effect. Similarly useful would be the photonic elementsdescribed in United States Patent Application 2010/027986 realized in ahyperuniform disordered material.

Applicants have also shown that hyperuniform disordered materials cansupport electromagnetic sensors that rely on waveguides. Thus, theguidance provided to make and use electromagnetic sensors based onwaveguides realized in photonic crystals also serves for constructingand using similar sensors realized in hyperuniform disordered materials.U.S. Pat. No. 7,731,902 (incorporated herein by reference for allpurposes) provides such guidance for an interferometric sensor, a sensorthat measures changes in the refractive index of a fluid, wherein thechanges are referable to the concentration of a target or analyte in thefluid, and a sensor having a photonic element whose refractive indexchanges as a result of the deposition of a target on the photonicelement or as a result of a binding of a target to the photonic element.

The distribution of dielectric material around bend junctions inbandgaps fashioned in the hyperuniform disordered materials is alwaysstatistically isotropic. Therefore, if the defect mode created by theremoval of material falls within the PBG, the bend can be oriented atany arbitrary angle. The light propagating through the unusually-shapedwaveguide channel simulated by removing dielectric cylinders along thesinusoidally-shaped path (FIG. 6) is tightly confined in the transversedirection, penetrating only in the next few rows of dielectriccylinders. Calculations showed that the transmission reached a maximumof about 83%. Back-scattering of the propagating mode, although likelyin such channels, can be alleviated by optimizing the cylinder sizealong the channel such that localized resonances similar to those thatarise in point-like defects “entrain” along the channel to guide lightthrough the channel.

The hyperuniform disordered structures analyzed here yielded largephotonic band gaps of around 40% of the central frequency. FIG. 14 showshigher-order guided modes obtained by varying the radius of the defectcylinders along the channel path.

The ability to construct waveguides oriented in virtually any directionallows the artisan to interconnect waveguides and cavities at junctionssuch that the interconnected channels can be in photonic communicationwith one another no matter what the relative orientations of thewaveguides. Moreover, each waveguide in the interconnected system can be“outfitted” with its own set of line defects and point defects, so thata system may serve as a means of splitting a band of frequencies intotwo or more sub-bands having selectable frequencies. Since thetransmission of each sub-band is independently tunable in each segmentof each waveguide, a photonic signal entering the system can benarrow-band filtered within any system to create a virtually unlimitednumber of specific systems. Highly advantageous in optical circuitdesign, for example, the designer has essentially unlimited flexibilityto design waveguides that accommodate any band structure and as muchflexibility in laying out the waveguide channels for any particularcircuit.

Cavity modes. According to recent unpublished simulation studies byFlorescu et al., introducing a point defect by removing a singledielectric cylinder from a 2D hyperuniform PBG structure results in alocalized cavity mode with monopole symmetry. The electric fieldoscillation pattern was predicted to extend 1-2 cell widths into thesurrounding structure (FIG. 9). When a defect dielectric cylinder ofincreasing radius was used to replace a regular one, the electric fieldof the localized cavity modes would oscillate with changing symmetries.For every symmetry order, such as monopole, dipole, quadrupole, hexapoleand octopole, it was observed that an increase in defect cylinder radiusintroduced higher resonant frequencies inside the PBG region. Cavitiesare easily generated and changed in this structure by removing rods tocreate voids and placing bundled clusters of rods into the voids. Hornantennas attached to a microwave vector network analyzer were used tomeasure the reflection and transmission through a slice of thehyperuniform disordered structure, a few wavelengths thick, with andwithout those cavities (FIG. 10).

The great flexibility in tuning these cavity modes in the hyperuniformdisordered structure, combined with its isotropy, makes it possible toguide and filter light of desired frequencies around arbitrarily sharpbends. FIG. 15 shows a photo of and transmission through a 50° bend,which can be considered as two straight channels joined by a cavity atthe corner. Waves of various frequencies prohibited from propagating inthe bulk PBG material PBG are guided and transmitted in the waveguidechannel through this sharp bend. The resonant frequencies in this cavitywere modified and optimized by adding and removing various rods. Thisflexibility and abundance of cavity modes are important for filteringand tuning applications.

Thus, sharp PBG resonant modes are shown by experiment to be attainablein a hyperuniform disordered structure, and the frequency of the modescan be tuned by varying the dielectric defects inside the cavity aspredicted by simulations. The ability to control and localize modes ofdifferent symmetry and frequency in the same physical cavity and toguide light through modes with different localization properties canhave a great impact on all-optical switching and single-atom lasersystems (Florescu, M. and John, S., Phys. Rev. A 69: 053810, 2004;Florescu, L. et al., Phys. Rev. A 69: 013816, 2004). The new cavity andwaveguide architectures are promising candidates for achieving highlyflexible and robust platforms for integrated optical micro-circuitry.

EXPERIMENTAL Example 1 Simulation

The finite-difference time-domain (FDTD) method (Yee, K., IEEE Trans.Antennas Propag. 14: 302 1966) was used to calculate the propagation oflight inside the hyperuniform disordered photonic structures. Acomputational domain with periodic boundary conditions in the transversedirection and perfectly matched layer (PML) condition in the normaldirection was employed. The spatial resolution in these numericalexperiments was at least n=64 mesh points per a, and the temporalresolution was 0.5/n×a/c, where c is the light speed in vacuum. Fortransmission calculations, a broadband source was placed at one end ofthe computational domain and the transmission signal was recorded at theother end with a line-detector (Oskooi, A., et al., Comp Phys. Comm.181: 687, 2010). The Fourier components of the field were then evaluatedand the spectra averaged and normalized to the transmission profile inthe absence of the structure. For quality factor calculations (Irvine,W., Phys. Rev. Lett. 96: 057405, 2006), the modes were excited with abroadband pulse from a current placed directly inside the cavity. Afterthe source was turned off, the fields were analyzed, and frequencies anddecay rates of the confined modes evaluated (Oskooi, A., et al., CompPhys. Comm. 181: 687, 2010). To calculate photonic band structures, asupercell approximation was employed using the conventional plane-waveexpansion method (Johnson, S. and Joannopoulos, J., Optics Express 8:173, 2001; Liang. W. et al., Phys. Rev. E 67: 026612, 2003).

FIG. 4 shows FDTD simulations of (left) TM and (right) TE band structure(blue and red curves) and DOS (green curve) for the hyperuniformstructure shown in FIG. 1a . The complete band gap region is shown bythe peach colored area. The PBGs shown are equivalent to the fundamentalband gap in periodic systems: the spectral location of the TM gap, forexample, is determined by the resonant frequencies of the scatteringcenters, and always occurs between band N and N+1, with N precisely thenumber of cylinders per supercell. Similarly, for TE polarized radiationthe band gap always occurs between bands N and N+1 where N is now thenumber of network cells in the structure.

In an otherwise unperturbed hyperuniform disordered structure, it ispossible to create a localized state of the electromagnetic field byreducing or enhancing the dielectric constant at a certain point in thesample. In two-dimensional structures, this can be realized by removingone of the cylinders. Due to the presence of the point-like defect, alocalized cavity mode is created within the photonic band gap at acertain frequency. FIG. 16a shows a cavity mode obtained by removing oneof the dielectric cylinders from a hyperuniform disordered structure.Note that the electric field distribution is highly localized around thedefect, extending only up to distances involving 1-2 rows of cylindersbeyond the position of the missing cylinder. The quality factor of thetwo-dimensional confined mode is higher than 10⁸. The nature of thelocalization mechanism around this type of defect in hyperuniformdisordered materials is rather different from the Anderson-likelocalization mechanism naturally present in this as well as conventionaldisordered structures. FIG. 16b shows a localized photonic mode in theunperturbed hyperuniform disordered structure has a localization lengththat is 5-6 times larger than that in the cavity mode.

In this system, the evolution of localized modes associated with acylinder perturbed by varying its radius can be tracked. When the radiusis reduced, a single mode from the continuum of modes below the lowerphotonic band edge is pulled inside the PBG and becomes localized. Ifthe radius of the cylinder is increased, a number of modes (the precisenumber is determined by the relative size of the defect cylinder) fromthe continuum of modes above the upper photonic band edge are pulledinside the PBG. FIG. 18 shows the electric field mode distribution for afew selected localized modes. Note the nearly perfect monopole (M),dipolar (D), quadrupolar Q), and hexapolar (if) symmetries associatedwith certain modes. Different localized modes are indexed based on theirapproximate symmetry (M,D,H, . . . ), where the first index refers tothe order of the mode and the second index refers to the number of modesof a given order (e.g., D1,2 is the second mode of first-order with adipole-like symmetry).

In FIG. 20 the evolution of the localized modes associated with a defectcylinder as a function of the dimensionless defect radius is tracked.The dimensionless defect radius in this example is r_(D)/r₀. For adefect radius r_(d)/r₀=0.47 (where r₀ is the radius of the unperturbedcylinders), the defect mode reaches the mid-point of the PBG and ismaximally protected from interactions with the propagating modes fromthe continua below and above the photonic band gap. When the radius ofthe defect cylinder is increased, it becomes possible to accommodatemore localized modes in the defect region, distinguished either by theirapproximate symmetry or frequency. For r_(D)/r₀=4, a total of 12localized modes can coexist within the same defect. However, it shouldbe noted that at these large radii, the defect cylinders start tooverlap with the surrounding cylinders and the confinement decreases.

In photonic crystals, removing a row of rods generates a channel throughwhich light with frequencies within the band gap can propagate, aso-called crystal waveguide. Light cannot propagate elsewhere in thestructure outside the channel because there are no allowed states. Thewaveguides must be composed of segments whose orientation is confined tothe high-symmetry directions of the crystal. As a result, the waveguidebends of 60° or 90° can be easily achieved, but bends at an arbitraryangle lead to significant radiation loss due to excessively strongscattering at the bend junction and require additional engineering tofunction properly.

Example 2: Construction of Disordered 2D Arrangements of DielectricMaterials with Bandgaps Comparable to Those in Photonic Crystals for theSame Dielectric Constant

The key features of the design are: (1) a disordered network ofdielectric cylinders and walls in which each cylinder is connected tothree neighbors (trivalency); and (2) the cylinder centers are generatedby a point pattern in which the number variance of points in a “window”of radius, R, σ(R)={N_(R) ²}−{N_(R)}² is proportional to R(hyperuniformity). Note that, for a 2D random Poisson distribution,σ(R)∝R² is proportional to the area, whereas crystals and quasicrystalshave σ(R)∝R. Because of these two features, the photonic design patternhas uniform nearest neighbor connectivity and hyperuniform long-rangedensity fluctuations or, equivalently, a structure factor with theproperty S(k)→0 for wavenumber k→0 (Torquato, S. and Stillinger, F.,Phy. Rev. E 68: 041113-1, 2003) similar to crystals; at the same time,the pattern exhibits random positional order, isotropy, and a circularlysymmetric diffuse structure factor S(k) similar to a glass. While it isnot necessary to propose any mechanism for how embodiments of aninvention work, and no such limitation is intended, it is believed thatthe novel combination of the foregoing characteristics enables Mieresonances in individual cylinders to couple in “bonding” and“antibonding” modes that concentrate electrical field either incylinders or in air cells separated by a band gap, reminiscent of theband edge states in the periodic crystals and in Si. Although thisExample focuses on 2D architectures, it is to be understood that thesame design principles can be applied to 3D architectures usingtechniques well-known to persons skilled in the art.

Example 3. “Stealthy” Systems

A subclass of 2D hyperuniform patterns comprise designs having thelargest band gaps for a given dielectric contrast (Florescu et al., PNAS106: 20658, 2009). These “stealthy” designs, as noted supra, have astructure factor S(k) precisely equal to zero for a finite range ofwavenumbers k<k_(C) for some positive k_(C). Stealthiness means thatintermediate as well as long-range density fluctuations are similar tocrystals. At the same time, when combined with the condition that thestructure be derived from a point pattern, increasing k_(C) results in anarrowing of the distribution of nearest-neighbor distances. The neteffect is to increase the band gap. This Example is the first physicalrealization of a hyperuniform stealthy design (FIG. 1) usingcommercially purchased Al₂O₃ cylinders and walls cut to designed heightsand widths. The dielectric constant of these Al₂O₃ materials wasmeasured to be 8.76 at the mid-gap frequency. The hyperuniform patternconsists of cylinders with radius r=2.5 mm connected by walls withthickness r=0.38 mm and various widths to match the hyperuniformnetwork; the components are 10 cm in the third dimension. The averageinter-cylinder spacing is a=13.3 mm and the sample size used in thetransmission measurements was 13a×13a, the region inside the red squarein FIG. 1(a). A platform in the desired hyperuniform pattern with slotsof depth 1 cm for the insertion of cylinders and walls was fabricated bystereolithography. A side view of the structure, FIG. 1(b), shows thepatterned platform and the inserted cylinders and walls. Cylinders andwalls can easily be removed and replaced to make cavities, waveguides,and resonance structures. FIG. 1(c) is a top view.

Samples for investigative use herein were fabricated by decoratinghyperuniform point patterns with cylindrical rods with dielectricconstant f=11.56 and radius r/a=0.189. These values were chosen tooptimize the size of the photonic band gap. The hyperuniform pointpatterns were generated using the collective coordinate method set forthin Torquato, S. and Stillinger, F., Phys. Rev. E 68: 04113, 2003 withstealthy order parameter χ=0.5. (Also appears in Description)

Experimentally, microwaves in the spectral range of 7-13 GHz, λ˜2a wereused, and a setup similar to the one described in Man, W., et al.Nature, 436: 993, 2005. The sample was placed between two facingmicrowave horn antennas. For band gap measurements, the horns were set adistance of 28a apart to approximate plane waves. Absorbing materialswere used around the samples to reduce noise. The transmission isdefined as the ratio between transmitted intensity with and without thesample in place. For the hyperuniform disordered structure shown in FIG.1b , measured transmission normal to the sample boundary was plotted inFIG. 2a (TE) and FIG. 2c (TM). The regions of low transmission agreewell with the calculated TE band gap (blue stripe in FIG. 2a ) and TMband gap (blue stripe in FIG. 2c ). The complete PBG region is where thetwo stripes overlap.

Example 4 Angular Dependence of the Photonic Properties

Cylinders and walls were removed from the corners of the samples toconstruct a circular boundary of diameter 13 a. The samples were rotatedalong the axis perpendicular to the patterned plane, and thetransmission was recorded every two degrees for both TE and TMpolarizations. In FIGS. 2e and f, 3D color plots of T(r=f, θ=θ) wereused in the cylindrical coordinate system (Man, W. et al. Nature 436:993, 2005) to present the measured transmission T as a function offrequency, f, and incident angle, θ. The results for the hyperuniformstructure show an isotropic complete PBG (circular blue ring) withrelative T<−20 dB at f=0.42 c/a, (c=light speed) for both polarizations.A similar square lattice was constructed and measured for comparison,shown in FIG. 5. Measured transmission as a function of frequencies(f=r) and incident angles (θ=θ) for the square lattice of (r=2.5 mm,t=0.38 mm, a=13.3 mm). In a) stop gaps due to Bragg scattering occur atthe Brillouin zone boundaries, change frequency in different directions,and do not overlap to form bandgap for TE polarization. In b) stop gapsshow angular dependence associated with 4-fold rotational symmetry, andare able to overlap in all directions for TM polarization. Through thesquare lattice, the measured TM polarization transmission is alsosignificantly lower than the TE polarization transmission.

The measured transmitted power was much lower for TM polarization thanfor TE polarization in both the hyperuniform sample and the squarelattice sample. For each polarization, the transmitted power was limitedby the horn geometry, namely the rectangular shape and the relativelysmall radiation acceptance angle of 15°.

The experimental results are compared with the theoretical predictionsobtained using a super-cell approximation and the conventionalplane-wave expansion method (Joannopoulos, J. et al. Photonic Crystals:Molding the Flow of Light (2^(nd) Ed.) Princeton University Press, 2008;Johnson S. and Joannopoulos, J., Optics Express 8: 173, 2001) tonumerically calculate the band structure of the system. The size of thesuper-cell applied for the simulation is 22a×22a as shown in entireregion of FIG. 1a . Finite difference time-domain (FDTD) simulations ofthe transmission spectrum through a finite sample of 22a×22a (bluecurves in FIG. 2 b and d) show regions of considerably reducedtransmission in the spectral region of the PBGs and overlap theexperimental results. Due to background dark noise (around −40 dB), theexperiment was limited to detecting a gap contrast of less than −30 dB,though the simulations of the finite sample indicated suppression by sixorders of magnitude. The calculated density of states (DOS) (greencurves in FIG. 2 b and d) for both TE and TM modes was zero within thePBG. Band structures for the TE and TM mode of the system are shown inFIG. 4.

Example 5 Waveguides

In order to test whether light can be guided through the hyperuniformdisordered structure, channels were created by removing two rows ofcylinders and walls along a line, as shown in FIG. 3a . The hornantennas were placed right next to the end of the channel for thetransmission measurement. For a completely open channel, without anydefect cylinders inside, the TM transmission spectrum is shown in FIG.3b , while the calculated TM polarization gap is highlighted withshading. Transmission through the channels is defined relative totransmission intensity between two facing horns separated by the channellength. A broad band of frequencies were guided through the open channelwith very high transmission. When a few roughly evenly spaced defectcylinders were placed inside the open channel, a sharp resonanttransmission peak appeared. Importantly, the resonant frequency in thesecoupled resonant waveguides can be easily tuned by modifying theposition of the defect cylinders. Two sets of defect cylinders marked asred or green dots in FIG. 3a were added separately. Their correspondingtransmission spectra are shown in FIG. 3c with red dash dot line orgreen dash line, respectively. The coupled resonator waveguide can befinely tuned acting as a narrow band pass filter with a high Q factor.

In photonic crystals, waveguides are limited in their direction andangularity by crystal symmetries (Lin, S-Y et al. Science 282: 274,1998). Without suggesting any limitation based on theories of whyembodiments of the invention work, it seems likely that the disorder andisotropy in the hyperuniform patterns relax many of the restrictionsfound in periodic structures. The flexibility of the experimental sampleemployed in these Examples makes it easy to form channels with arbitrarybending angles and to decorate their sides, corners and centers withcylinders and walls for tuning and optimizing the transmission bands.FIG. 3d shows a waveguide with a sharp 50° bend made by removingcylinders and walls in a path ˜2a wide. FIG. 3e shows the measuredtransmission. The transmission is comparable to that in the straightchannel with unity transmission despite the sharp bend, and it isadjustable by modifying defects. Even more remarkable is the “S” shapedfreeform waveguide shown in FIG. 3f . As in the previous channels, thetransmitting and receiving horns are parallel to the input and output ofthe channel and the transmission is of order unity (FIG. 3g ). Again,transmission bands can be easily improved and flexibly tuned usingdefect cylinders.

The foregoing Examples have experimentally demonstrated for the firsttime three significant results. First, an isotropic complete PBG wasobtained, Δf/f=4.0%, (all angles and all polarizations) in a 2Ddisordered hyperuniform dielectric material at dielectric contrast of8.76. Unlike photonic crystals, the sample material is disordered andhyperuniform, lacking long-range translational order and Braggscattering, yet results in isotropic photonic bandgaps. Furthermore, theisotropic PBG permitted fabrication of freeform waveguides impossiblefor photonic crystals. The freeform guides can channel photons robustlyin arbitrary directions with facile control of transmission bandwidthand sharp filtering. Finally, the waveguides can be decorated to producesharp resonant structures. These phenomena illustrate the potential ofhyperuniform disordered structures for producing photonic, phononic andelectronic materials with novel physical properties and technologicalapplications.

Example 6: Frequency Splitters and Narrow-Band Filters

FIG. 7 shows a “Y” shape junction for frequency splitting. Continuouswaves of different frequencies were sent into the input port marked as“1” on the photo. Transmissions were measured separately at twodifferent output ports marked as “2” and “3”, respectively. At the sametime, signals of different frequencies were directed into differentbranches automatically. The disordered hyperuniform PBG material offersa very flexible platform for defect design to select tunablefrequencies, therefore the transmission peaks through two branches ofthe “Y” shape junction can be controlled and tuned by arrangingdifferent distribution of extra defect cylinders in the two outputbranches.

FIG. 8 a) and b) show a two-step frequency splitter, c) and d) athree-way frequency splitter. Again, signals of different frequenciesare automatically directed into different branches in variousarchitectures. The propagating modes are strongly related to resonancesbuilt up inside the channel, enabling us to design local defects tocontrol the passing frequency of each channel.

Experimentally, stereolithography was used to fabricate the bases of thestructures at the scale of average spacing a=13.3 mm. Commerciallyavailable 100.0 mm tall Al₂O₃ cylinders of radius r=2.5 mm and thinsheets of thickness t=0.38 mm of various width were used to assemble thehyperuniform network structure. The photonic properties were measuredusing a HP-8510C vector network analyzer for microwaves with wavelengthcomparable to twice the cylinder spacing. The structure has a TMpolarization PBG from 9.2 to 10.7 GHz and a TE polarization PBG from 8.7to 9.6 GHz. Wave-guiding channels were constructed and modified byremoving rows of building blocks and adding individual extra defectcylinders. Transmission through the channels was measured by placing twomicrowave horn antennas right next to the channel openings. Absorptionmaterials were placed around the sample to reduce noise.

The experiments have demonstrated novel architectures for freeformwaveguides of arbitrary shapes, as well as compact frequency splitterswith flexible tuning abilities, in isotropic PBG material. The abilityto guide and split EM waves in a freeway format make this new class ofdisordered PBG materials good candidates for achieving highly flexibleand robust platforms for integrated optical and other electromagneticcircuits.

Example 7: Cavity Architectures

The experimental structure (FIG. 9) for this example was assembled usingAl₂O₃ cylindrical rods (r=2.5 mm, h=10 cm), inserted into a platform ofa hyperuniform disordered pattern with 1 cm deep slots. The average cellsize (spacing between rods) was a=13.3 mm. The structure had TMpolarization PBG of 9.2 to 10.7 GHz. Cavities were easily generated andchanged in this structure by removing rods to create voids and placingbundled clusters of rods into the voids. Horn antennas attached to amicrowave vector network analyzer were used to measure the reflectionand transmission through a slice of the hyperuniform disorderedstructure, a few wavelengths thick, with and without those cavities(FIG. 10).

As shown in FIG. 11, cavity modes were revealed by large transmissionpeaks inside the PBG frequency region. By removing two cylinders in themiddle of the structure, cavity modes around 10.3 GHz were excited. Thetransmission peaks associated with those cavity modes decreasedexponentially with the thickness of the sample slice, and still remaineddetectable when the cavities were at a distance of 2.5a away from thesample edge.

To investigate the symmetry properties of the cavity modes, bundledclusters of alumina rods were introduced in different arrangements andorientations. As was predicted in the simulation study, an increase ofthe high-index dielectric defect radius pushed the resonant frequencyhigher for a particular order of symmetry mode. As shown in FIG. 12,introducing a 3-rod, 4-rod, and 7-rod cluster, respectively, resulted invarious resonant peaks of different cavity modes.

The great flexibility in tuning these cavity modes in the hyperuniformdisordered structure, combined with its isotropy, makes it possible toguide and filter light of desired frequencies around arbitrary sharpbends. FIG. 13 shows a photo of and transmission through a 50° bend,which can be considered as two straight channels joined by a cavity atthe corner. Waves of various frequencies inside the PBG were guided andtransmitted through this sharp bend. The resonant frequencies in thecavity were modified and optimized by adding and removing various rods.This flexibility and abundance of cavity modes are important forfiltering and tuning applications.

The results demonstrate that sharp PBG resonant modes are attainable ina hyperuniform disordered structure, and the frequency of the modes canbe tuned by varying the dielectric defects inside the cavity aspredicted by simulations. The ability to control, localize, and slowdown EM waves inside solids will have a great impact on futuretechnological development of optical and other electromagnetic switches,lasers and sensors.

The references cited throughout this application are incorporated forall purposes apparent herein and in the references themselves as if eachreference was fully set forth. For the sake of presentation, specificones of these references are cited at particular locations herein. Acitation of a reference at a particular location indicates a manner inwhich the teachings of the reference are incorporated. However, acitation of a reference at a particular location does not limit themanner in which all of the teachings of the cited references areincorporate for all purposes.

Additional embodiments include any single embodiment herein supplementedwith one of more element from any one or more other embodiment herein.

It is understood, therefore, that this invention is not limited to theparticular embodiments disclosed, but is intended to cover allmodifications which are within the spirit and scope of the invention asdefined by the appended claims and the above description.

1-14. (canceled)
 15. A designed cavity fabricated in a hyperuniformdisordered phononic material having a complete phononic bandgap, whereinthe cavity confines a phonon.
 16. The method of claim 15, whereinacoustic waves cannot propagate in said cavity.
 17. The method of claim15, wherein elastic waves cannot propagate in said cavity.
 18. Themethod of claim 15, wherein said phononic material comprises elasticmaterial.
 19. A designed waveguide fabricated in a hyperuniformdisordered phononic material having a complete phononic bandgap, whereinthe waveguide confines the propagation of a phonon.
 20. The method ofclaim 19, wherein acoustic waves cannot propagate in said completephononic bandgap.
 21. The method of claim 19, wherein elastic wavescannot propagate in said complete phononic bandgap.
 22. The method ofclaim 19, wherein said phononic material comprises elastic material. 23.A plurality of waveguides disposed at arbitrary angles with respect toone another in phononic communication.
 24. The method of claim 23,wherein the communication takes place at a junction of the waveguides.25. The method of claim 24, wherein the junction comprises a phononiccavity that communicates with the waveguides.
 26. The method of claim24, wherein a spectrum of acousto-elastic waves enters through one armand is divided at the junction into different frequency bands, each ofwhich is directed into different arms.